PLEASE HURRY!!!
WILL MARK!!!
Which statement describes a difference between the lower mantle and oceanic crust?
Answer:
Its C on edge
Explanation:
trust me
A displacement vector points in a direction of θ = 23° left of the positive y-axis. The magnitude of this vector is D = 155 m. Refer to the figure. Enter an expression for the x-component vector, Dx, in terms of D, θ, and the unit vectors i and j.
Answer:
Dₓ = -155 sin 23° i + 0 j
Explanation:
The diagram showing the vector has been attached to this response.
As shown in the diagram,
The vector D has an x-component (also called horizontal component) of -D sinθ i. i.e
Dₓ = -D sin θ i [The negative sign shows that D lies in the negative x direction]
Where;
D = magnitude of D = 155m
θ = direction of D = 23°
Therefore;
Dₓ = -155 sin 23° i
Since Dₓ represents the x component, its unit vector, j component has a value of 0.
Therefore, Dₓ can be written in terms of D, θ and the unit vectors i and j as follows;
Dₓ = -155 sin 23° i + 0 j
The x-component of the vector is written as [tex]D_x = (-60.56 \ i + 0j)\ m[/tex].
The given parameters;
direction of the vector, θ = 23°magnitude of the vector, D = 155 mThe x-component of the vector is calculated as;
[tex]D_x = D \ \times sin\theta \\\\D_x = 155 \times sin(23)\\\\D_x = 60.56 \ m[/tex]
Since the direction of the vector is in negative x-axis, the x-component of the vectors is written as;
[tex]D_x = (-60.56 \ i + 0j)\ m[/tex]
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Show that a tilted linearly polarized wave can be written as the sum of LCR and RCP.
Answer:
E_{z} = E_{z} (RCP) + E_{z} (LCP)
E_{z} = 2 E₀ cos (kz-wt) i^
Explanation:
An electromagnetic wave is said to be polarized if the electric field for a fixed point in space has a definite direction in time.
Based on this definition we can define some types of polarization; Linear; right-hand, left-hand circular, and elliptical
Circular polarization is that for a fixed point in space, the electric field describes a circle in time, if this circle rotates clockwise it is called right circular polarization (RCP) and if it rotates counterclockwise it is called polarization left circular (LCP)
For wave moving in the z direction the electric fields must oscillate in the x or y direction
for right-hand circular polarization (RCP)
[tex]E_{z}[/tex] = E₀ cos (kz -wt) i^ + E₀ sin (kz -wt) j^
for left circular polarization (LCP)
E_{z} = E₀ cos (kz -wt) i ^ - E₀ sint (kz -wt) j ^
linear polarization can be obtained if we add these two polarizations
E_{z} = Ez (RCP) + Ez (LCP)
E_{z} = E₀(cos (kz -wt) i^ + sint (kz -wt) j^ + cos (kz -wt) i^ - snt (kz -wt)j^ )
E_{z} = 2 E₀ cos (kz-wt) i^
the latter is a linear polarization on the x axis
A single atom of an element has 11 protons, 11 electrons, and 12 neutrons. Which element is it?
Оy
O Na
OMg
O Se
The magnitude of average acceleration in half time period in a simple harmonic motion is
(A) 2 ω2A /π
(B) ω2A /2 π
(C) ω2A /√2 π
(D) Zero
Answer:
Option A - 2ω²A/π
Explanation:
The displacement of simple harmonic motion is usually given as;
x = Asinωt
Where;
A is amplitude
ω is angular frequency
Now, average acceleration in half time period is given as;
a_av = d²x/dt² = -ω²A sinωt
Thus;
a_av = ∫a(t)dt/(∫dt) with both numerator and denominator between the boundaries of T/2 and 0.
Full expression gives;
(2/T)(ω²A∫sin(ωt) dt between the boundaries of T/2 and 0.
Now, integrating gives;
(2/T)(ω²A × 1/ω)[-cos(ωt)] between the boundaries of T/2 and 0.
Plugging in the boundary conditions gives us;
(2/T)(ω²A × 1/ω)[-cos(ωT/2) + cos0]
Simplifying gives;
(2ωA/T)[-cos(ωT/2) + 1]
In simple harmonic motion, we know that ω = 2π/T
Thus we have;
(2ωA/T)[-cos(2π/2) + 1]
(2ωA/T)[-cos(π) + 1]
This gives;
(2ωA/T)[1 + 1]
= (4ωA/T)
Now, from earlier ω = 2π/T
Thus, T = 2π/ω
So, we have;
a_av = (4ωA/(2π/ω))
a_av = 2ω²A/π
It was once recorded that a Jaguar
left skid marks that were 290 min
length. Assuming that the Jaguar
skidded to a stop with a constant
acceleration of -8.90 m/s2,
determine the speed of the Jaguar
before it began to skid.
Answer:
71.85 m/s
Explanation:
Given the following :
Length of skid marks left by jaguar (s) = 290 m
Skidding Acceleration (a) = - 8.90m/s²
Final velocity of jaguar (v) = 0
Speed of Jaguar before it Began to skid =?
Hence, initial speed of jaguar could be obtained using the formula :
v² = u² + 2as
Where
v = final speed of jaguar ; u = initial speed of jaguar(before it Began to skid) ; a = acceleration of jaguar ; s = distance /length of skid marks left by jaguar
0² = u² + (2 × (-8.90) × 290)
0 = u² + (-5,162)
u² = 5162
Take the square root of both sides
u = √5162
u = 71.847 m/s
u = 71.85m/s
Emily wanted to see what battery lasted the longest. She put each battery into a clock and recorded the time that the clock stopped. She used Duracell, Energizer, Kroger brand, and EverReady. Iv,Dv, Control, consistent
Answer:
This question is asking to identify the following variables:
Independent variable (IV): Battery
Dependent variable (DV): Time the clock stopped
Constant: Same clock
Control: No stated control
Explanation:
The independent variable in an experiment is the variable that is subject to manipulation or change by the experimenter. In this experiment, the independent variable is the BATTERIES (Duracell, Energizer, Kroger brand, EverReady).
The dependent variable is the variable that responds to the changes made to the independent variable. It is the variable that the experimenter measures. In this case, the dependent variable is the TIME IT TAKES FOR THE CLOCK TO STOP.
Constants or control variable is the variable that the experimenter keeps constant or unchanged for all groups throughout the experiment in order not to influence the outcome of the experiment. The constant in this case is the SAME CLOCK USED.
Control group is the group that does not receive the experimental treatment or independent variable in an experiment. In this case, all groups received a different kind of battery.
The energy stored in a wooden log transforms when the log is burned. Which of the following explanations BEST describes how the chemical energy stored in the log compares to the heat and light energy produced by burning?
A. chemical energy is the same and additional energy is produced as heat and light.
B. chemical energy is more than the amount of heat and light
C. the amount of chemical energy is less than the amount of heat and light energy
D. the amount of chemical energy equals the amount of heat and light energy.
Answer:
D. the amount of chemical energy equals the amount of heat and light energy.
Explanation:
Given that the first law of thermodynamics affirmed that energy is neither created nor destroyed however, it can be transformed from one form to another. In other words, while, during the transformation of energy, no energy is lost, the input energy is also equal to output energy.
Hence, the chemical energy stored in the log is EQUAL to the heat and light energy produced by burning.
Which of the following are evidence of what happened in the past?
A.
volcanoes and plate movement
B.
weathering and rain
C.
weather and erosion
D.
earthquakes and climate
Answer:
A
Explanation:
volcanoes and plate movement
An eagle is flying horizontally at a speed of 3.80 m/s when the fish in her talons wiggles loose and falls into the lake 3.90 m below. Calculate the velocity (in m/s) of the fish relative to the water when it hits the water. (Assume that the eagle is flying in the x-direction and that the y-direction is up.)
Answer:
the velocity of the fish relative to the water when it hits the water is 9.537m/s and 66.52⁰ below horizontal
Explanation:
initial veetical speed V₀y=0
Horizontal speed Vx = Vx₀= 3.80m/s
Vertical drop height= 3.90m
Let Vy = vertical speed when it got to the water downward.
g= 9.81m/s² = acceleration due to gravity
From kinematics equation of motion for vertical drop
Vy²= V₀y² +2 gh
Vy²= 0 + ( 2× 9.8 × 3.90)
Vy= √76.518
Vy=8.747457
Then we can calculate the velocity of the fish relative to the water when it hits the water using Resultant speed formula below
V= √Vy² + Vx²
V=√3.80² + 8.747457²
V=9.537m/s
The angle can also be calculated as
θ=tan⁻¹(Vy/Vx)
tan⁻¹( 8.747457/3.80)
=66.52⁰
the velocity of the fish relative to the water when it hits the water is 9.537m/s and 66.52⁰ below horizontal
3. Does the Sun's light that reaches Earth produce a true continuous rainbow? If not, what colors
would you expect our sun's light to be missing if the outer atmosphere is pure Hydrogen?
Answer:
when there is no water in the atmosphere or when no drops are formed there is no rainbow..
he hydrogen transition lines would be missing in the visible range, the RED region
Explanation:
The sunlight that reaches the Earth is scattered by the atmosphere and radiated, as the atmosphere has mainly nitrogen, the radiated light is blue, this light does not produce a rainbow.
The sunlight must reach a drop of water that disperses the colors according to the refractive index of the water and in this way produces a rainbow, so when there is no water in the atmosphere or when no drops are formed there is no rainbow..
If the atmosphere were composed of Hydrogen, the hydrogen transition lines would be missing in the visible range, this corresponds to the so-called Balmer series and they are in the RED light region.
How is it possible charge electrical devices when the power is out?
Answer:
generator
Explanation:
it can run an electric current to an outlet and let it charge
1. Classify What type of heat transfer occurs
when you roast a marshmallow by holding it
campfire?
over a co
Answer:
Convection
Explanation:
because it tis the transfer of energy through a fluid or gas
When you roast a marshmallow by holding it campfire, the heat transfer in the process of radiation.
What is thermal radiation ?Thermal radiation is a process in which energy, in the form of electromagnetic radiation, is emitted from a heated surface in all directions and moves at the speed of light directly to its site of absorption. Thermal radiation does not move through an intermediary medium.
From the longest infrared rays through the visible light spectrum to the shortest ultraviolet rays, thermal radiation spans the entire electromagnetic spectrum. The temperature of the emitting surface controls the distribution and intensity of radiant radiation within this range.
When you roast a marshmallow by holding it campfire, the heat transfer by the process of radiation through air.
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Question 2 (1 point)
The direction of the result of the cross product of two vectors is perpendicular to the
plane containing the two vectors, specified by the right hand rule.
True
ОО
False
A moving roller coaster speeds up with constant acceleration for 2.3\,\text{s}2.3s2, point, 3, start text, s, end text until it reaches a velocity of 35\,\dfrac{\text{m}}{\text{s}}35 s m 35, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction. During this time, the roller coaster travels 41\,\text{m}41m41, start text, m, end text. We want to find the initial velocity of the roller coaster before it starts to accelerate. Which kinematic formula would be most useful to solve for the target unknown?
Answer:
Δx=(v+v0/2)t
Explanation:
We can figure out which kinematic formula to use by choosing the formula that includes the known variables, plus the target unknown.
In this problem, the target unknown is the initial velocity v_0v
0
v, start subscript, 0, end subscript of the roller coaster.
A raft is made using a number of logs (TBD) with 25-cm diameter and 2-m-length. It is desired that a maximum 90 percent volume of each log will be submerged when carrying two boys with 400 N each. Determine the minimum number of logs that must be used. The specific gravity of the log is 0.75.
Answer:
6logs
Explanation:f
First finding the volume of the logs
V= π/4d²l
= 0.098m³
So number of logs will be
Weight of 2 boys + weight of log = buoyancy force.
So
2( 400)+ N ( Mlog x g) = density of water x volume displaced x g
2(400) = N x 0.098x 1000x 9.8 x 0.9- 0.75* 1000
N= 5.5 which is approx 6logs
The minimum number of logs that must be used is 6 logs.
Calculation of the number of logs:Here first determine the volume of the logs i.e.
V= π/4d²l
= 0.098m³
Now
number of logs will be
Weight of 2 boys + weight of log = buoyancy force.
2( 400)+ N ( Mlog x g) = density of water x volume displaced x g
2(400) = N x 0.098x 1000x 9.8 x 0.9- 0.75* 1000
N= 5.5
= 6logs
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11. Angie runs around a circular track for 20mins. The track is 1km and she runs at a rate of
1km10min. What is her total displacement?
a. 2km counterclockwise
b. 0.1km
c. 2km clockwise
d. Okm
e. 2km
Answer:
0 km
Explanation:
Since she is running in a circle, her final position is where she started which is at 0 km.
0km is her total displacement. So, the correct option is (D).
What is Displacement?Displacement is described as a change in the position of an object which is a vector quantity and has a direction and a magnitude. It is represented as an arrow pointing from the starting position to the final position. For example- If an object moves from position A to position B, then the position of the object changes.
Displacement is defined as the shortest distance from the initial position to the final position of the object. For above given information, Angie is running in a circle, so her final position is where she started which is at 0 km.
Thus, 0km is her total displacement. So, the correct option is (D).
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100 POINTS.
PLEASE EXPLAIN YOUR ANSWER.
Explanation:
Draw free body diagrams for each mass.
There are 3 forces on the disk: weight force mg pulling down, normal force N pushing up, and tension force T pulling right.
There are 2 forces on the cylinder: tension force T pulling up and weight force 3mg pulling down.
Sum of forces on the disk in the centripetal direction:
∑F = ma
T = m v²/r
Sum of forces on the cylinder in the vertical direction:
∑F = ma
T − 3mg = 0
T = 3mg
Substituting:
3mg = m v²/r
3gr = v²
v = √(3gr)
Plug in values:
v = √(3 × 10 m/s² × 0.800 m)
v = √24 m/s
v ≈ 4.90 m/s
5. Carey and Heather wanted to know if the size of a coin will affect the number of drops of water it can hold. So they used a dropper to place water on a quarter, nickel, and penny. a. Question: b. Hypothesis + Prediction: c. Independent Variable (IV): d. Dependent Variable (DV): e. Controlling Variable (CV): f. Experiment:
Answer:
the correct answer is f EXPERIMENT
Explanation:
In this exercise on these young people we want to know to which part of the scientific method their statement corresponds.
In order to answer, we must describe the main parts of the scientific method.
* Question. It is a question that we unleash to answer
* Hypothesis. It is an assumption that we want to check
* Independent variable. It's the thing that researcher controls
* dependent variable . It is the magnitude is measured
* Experiment. It is the design of a methodology to test the hypothesis.
In this case, the young people describe a procedure to test a hypothesis, so this part corresponds to an EXPERIMENT
the correct answer is f
Two trains, each having a speed of 33 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h flies off the front of on train when they are 60 km apart and heads directly for the other train. On reaching the other train, the (crazy) bird flies directly back to the first train, and so forth. What is the total distance the bird travels before the trains collide?
Answer:
66 km
Explanation:
Given that:
The speed of the two trains = 33 km/h
The speed of the bird = 60 km/h
The distance apart between the two trains = 60 km
From the given information, we are being told that the two trains are going at the same speed. Therefore, they will definitely collide at 30 km
We know that:
speed of the train = distance traveled × time
Making the time t the subject of the formula:
time = speed of the train / distance traveled
time = 30 km / 33 km/h
time = 0.909 / hr
Thus, the bird flying at a given speed of 60 km/h in a time of 0.909 / hr will cover a total distance of :
distance (d) = speed of the bird/ time
distance (d) = [tex]\dfrac{60 \ km/hr}{0.909 \ /hr}[/tex]
distance (d) = 66 km
What is the minimum amount of energy required to completely melt a 7.25-kg lead brick which has a starting temperature of 18.0 °C? The melting point of lead is 328 °C. The specific heat capacity of lead is 128 J/(kg∙C°); and its latent heat of fusion is 23,200 J/kg.a. 1.68 × 105 J b. 2.88 × 105 J c. 4.56 × 105 J d. 5.96 × 105 J e. 7.44 × 105 J
Answer: c. 4.56 × 105 J
Explanation:
Given that
mass of lead brick, m= 7.25kg
Temperature T1 = 18.0 °C
Temperature T2 = 328 °C
specific heat capacity of lead, c = 128 J/(kg∙C°)
latent heat of fusion Lfusion =23,200 J/kg
Amount of energy Q =?
Using the formulae
Amount of energy ,Q =mc ( T2-T1)+ mLfusion
7.25kg x 128 J/(kg∙C°) x (328-18°C) + 7.25kg x 23200 J/kg
=455880J
=4.56 x 10^5 J
The minimum amount of energy required is 4.56 × 10^5 J.
Calculation of the minimum amount of energy:Since
mass of lead brick, m= 7.25kg
Temperature T1 = 18.0 °C
Temperature T2 = 328 °C
specific heat capacity of lead, c = 128 J/(kg∙C°)
latent heat of fusion =23,200 J/kg
So
we know that
Amount of energy ,Q =mc ( T2-T1)+ mLfusion
7.25kg x 128 J/(kg∙C°) x (328-18°C) + 7.25kg x 23200 J/kg
=455880J
=4.56 x 10^5 J
hence, The minimum amount of energy required is 4.56 × 10^5 J.
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At a painfully loud concert, a 120-dB sound wave travels away from a loudspeaker at 343 m/s.
How much sound wave energy is contained in each 1.0-cm^3 volume of air in the region near this loudspeaker?
Answer:
2.9*10^-9 J
Explanation:
Given that sound level is B= 120dB
And B=10log(Io/I)
And I = (10^12)Io
So I = 1W/m²
So to find Energy
∆E= I∆V/v
Where ∆V= 1*10-6m³
v = 343
So ∆E=2.9*10^-9 J after substituting the values
Is rock a substance or homogeneous or heterogeneous
Answer:
substances is ur answer dear mate
comment in the comment section
Answer: A rock is a substance.
Explanation: Rock is a substance because a rock does no have genes like you and I. And most rocks are made of sediment. That have been compressed together overtime.
When a current of 0.015 A passes through human body at 240 volts p.d it
causes
Explanation:
Given that,
Current, I = 0.015 A
Voltage, V = 240 volts
We need to find the resistance. Using Ohm's law we can find it as follows :
[tex]V=IR\\\\R=\dfrac{V}{I}\\\\R=\dfrac{240}{0.015}\\\\R=16000\ \Omega[/tex]
So, When a current of 0.015 A passes through human body at 240 volts p.d it causes 16000 ohms of resistance.
7. Solve (3.96 x 10^2)/(1.6 x 10^-8). Be
sure your answer is in scientific notation.
Round to two decimal places.
(1 Point)
Enter your answer
Answer:
[tex]2.48*10^{10}[/tex]
Explanation:
Given the expression (3.96 x 10^2)/(1.6 x 10^-8), we are to express in scientific notation. Applying one of the laws of indices which says;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
The expression becomes;
[tex]= \dfrac{3.96}{1.6}*\dfrac{10^2}{10^{-8}}\\ \\= \dfrac{3.96}{1.6}*10^{2-(-8)}\\\\= \dfrac{3.96}{1.6}*10^{2+8}\\\\= \dfrac{3.96}{1.6}*10^{10}\\\\= 2.475*10^{10}\\\\= 2.48*10^{10} (to \ 2dp)[/tex]
Consider two positively charged particles, one of charge q0 (particle 0) fixed at the origin, and another of charge q1 (particle 1) fixed on the y-axis at (0,d1,0). What is the net force F⃗ on particle 0 due to particle 1? Express your answer (a vector) using any or all of k, q0, q1, d1, i^, j^, and k^.
Answer:
[tex]F_{10} = - \frac{k_{q1}* qo }{d_{1} ^{2} } j[/tex]
Explanation:
The net force ( F ) on particle 0 due to particle 1 can be expressed as
[tex]F_{10} = \frac{K_{q1}*qo }{r_{10} ^{3} } r_{10}[/tex]
k = coulomb constant
[tex]r_{10}[/tex] = distance between charge o and charge 1
to get the vector form ( attached below ) we substitute [tex]d_{1}[/tex] for [tex]r_{10}[/tex] and [tex]- d_{1} j[/tex] for [tex]r_{10}[/tex]
The net force on [tex]q_{0}[/tex] by [tex]q_{1}[/tex] is , [tex]F=-K\frac{q_{0}*q_{1}}{r^{2} }j[/tex]
The force between two charges is given by Coulomb force law.
[tex]F=K\frac{q_{0}*q_{1}}{r^{2} }[/tex]
Where K is Coulomb constant, [tex]K=9*10^{9}Nm^{2}/C^{2}[/tex]
and r is the distance between both charges.
Here given that, [tex]q_{0}[/tex] is located as (0, 0, 0) and [tex]q_{1}[/tex] is located at [tex](0,d_{1}, 0)[/tex]
The force on [tex]q_{0}[/tex] by [tex]q_{1}[/tex] in the negative y - axis.
So that , Direction of force is, [tex]-j[/tex]
Hence, the net force on [tex]q_{0}[/tex] by [tex]q_{1}[/tex] is , [tex]F=-K\frac{q_{0}*q_{1}}{r^{2} }j[/tex]
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launch a rocket ship weighs 4.5 million pounds. When it is launched from rest, it takes 8.00 s to reach 164 km/h ; at the end of the first 1.00 min , its speed is 1640 km/h . Part APart complete What is the average acceleration (in m/s2) of the rocket during the first 8.00 s? aav = 5.69 m/s2 Previous Answers Correct Part BPart complete What is the average acceleration (in m/s2) of the rocket between 8.00 s and the end of the first 1.00 min? aav = 7.88 m/s2 Previous Answers Correct Part CPart complete Assuming the acceleration is constant during each time interval (but not necessarily the same in both intervals), what distance does the rocket travel during the first 8.00 s? Express your answer with the appropriate units. x = 182 m Previous Answers Correct Part D Assuming the acceleration is constant during each time interval (but not necessarily the same in both intervals), what distance does the rocket travel during the interval from 8.00 s to 1.00 min? Express your answer with the appropriate units.
Answer:
A) a_av = 5.695 m/s²
B) a_av = 7.88 m/s
C) x_f = 182.24 m
D) x_f = 13029.12 m
Explanation:
A) Initial velocity at 0 seconds; v_i = 0 m/s
Final velocity at 8 seconds;v_f = 164 km/h = 45.56 m/s
So, formula for average acceleration is;
a_av = change in velocity/change in time.
Thus, for the first 8 seconds;
a_av = (45.56 - 0)/(8 - 0)
a_av = 45.56/8
a_av = 5.695 m/s²
B) From part A, we now want to find the average acceleration from 8 seconds to 1 minute (60 seconds)
After the 60 seconds, the speed is 1640 km/h = 455.56 m/s
Thus;
Average acceleration is;
a_av = (455.56 - 45.56)/(60 - 8)
a_av = 7.88 m/s
C) Now we are told the acceleration is constant and we want to find the distance the rocket travels during the first 8 seconds.
So, distance formula we will use is;
x_f = x_i + ½(v_i + v_f)t
So at this stage, v_i = 0 m/s and v_f = 45.56 m/s and x_i = 0 m
Thus;
x_f = 0 + ½(0 + 45.56)8
x_f = 182.24 m
D) Now we want to find the distance the rocket travels during the 8 seconds to 1 minute (60 seconds) interval.
From part B, v_i = 45.56 m/s and v_f = 455.56 m/s
Also, x_i = 0 while time interval(t) = 60 - 8 = 52 s
Thus;
x_f = 0 + ½(45.56 + 455.56)52
x_f = 13029.12 m
Average speed is calculated by dividing the?
Explanation:
Hey there!
By dividing "total distance" by "time taken".
Reason: From formula.
[tex]average \: speed = \frac{total \: distance}{time \: taken} [/tex]
Hope it helps...
A 10 kg package is delivered to your house. Use one complete sentence to describe an example of how work is done on the package as it gets brought inside. Make sure to use proper spelling, grammar, and other language mechanics. In your explanation, make sure to use the terms related to the formula for work (W = Fd).
Answer:
Hey :)
Explanation:
Work is a net force applied through a distance in order to displace an object, commonly abbreviated as W. A net force is the sum of all forces acting on an object. Work is mass times acceleration and distance so to find out the work you simply calculate the acceleration of the box being brought in. Next find the distance it was carried to get in the house. Then find out the mas of the box and finally multiply those sums together to get the amount of work put in to bring the package inside.
hope this helps :) xo
By what factor is the heat flow increased if a window 0.550 mm on a side is inserted in the door? The glass is 0.450 cmcm, and the glass has a thermal conductivity of 0.80 W/(m⋅K)W/(m⋅K). The air films on the two sides of the glass have a total thermal resistance that is the same as an additional 12.0 cmcm of glass.
This question is incomplete, the complete question is;
A carpenter builds a solid wood door with dimensions 1.95 m × 0.99 m × 4.5 cm . Its thermal conductivity is k=0.120W/(m.K). The air films on the inner and outer surfaces of the door have the same combined thermal resistance as an additional 1.6 cm thickness of solid wood. The inside air temperature is 19.0°C , and the outside air temperature is -6.50°C .
a) What is the rate of heat flow through the door?
b) By what factor is the heat flow increased if a window 0.550 m on a side is inserted in the door? The glass is 0.450 cm , and the glass has a thermal conductivity of 0.80 W/(m.K). The air films on the two sides of the glass have a total thermal resistance that is the same as an additional 12.0 cm of glass.
Answer:
a) the rate of heat flow through the door is 97 watts
b) The factor of increased heat flow is 1.353
Explanation:
Given that;
room dimension = 1.95m × 0.99m × 4.5cm,
thermal conductivity = 0.120 w/m.k
additional thickness of solid wood Δt = 1.6 cm
a)
first we determine the effective thickness of the door;
t = 4.5cm + 1.6 cm = 61 cm ≈ 0.061 m
Now rate of heat flow is given by the relation
Q = KA( (TH -TC)/L)
= 0.12 × (1.95 m × 0.99 m) × ( (19°C - (-6.50°C)) / 0.061m)
= 0.23166 × 418.0327
= 96.8414 watts
Q = 97 watts
therefore the rate of heat flow through the door is 97 watts
b)
by intensity the glass of thickness 0.450 cm
the effective thickness is
L = 0.45cm + 12 cm = 12.45 cm = 0.1245 m
additionally area of glass A = (0.550 m)²
A = 0.3025 m²
Now
Qglass = KA ((TH-TC)/L)
= 0.80 w/m.k × 0.3025 m² × (19°C - (-6.50°C)) / 0.1245m)
= 0.242 × 204.819
Qglass = 49.57 watt
Qwood = KA ((TH-TC)/L)
area of wooden door = (1.95×0.99) - 0.3025 m² = 1.628m²
so Qwood = 0.12 × 1.628 × (19°C - (-6.50°C)) / 0.061m)
= 0.19536 × 418.0327
Qwood = 81.67 watt
Q = Qglass + Qwood
Q = 49.57 watt + 81.67 watt
Q = 131.24 watt
The factor of increased heat flow is;
f = 131.24 watt / 97 watts
f = 1.353
